profcyclist the logic is , when you play a song and stop it it has 3 options as you stop it auto starts from beginning if you start , it pauses and continues or it jumps to end of song and automatically either plays the next song or just waits for your command to start, this all depends on how you have setup things in your settings.
If you have used trim on a song then it jumps to the trim position setting.
Whenever you choose another song and get back to your last song it starts from the beginning of that song it assumes you need to start from beginning every time so to answer your question no it will not remember your song position wherever you leave a song it will always start from beginning.